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A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models

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  • Çayan, Seda
  • Özhan, B. Burak
  • Sezer, Mehmet

Abstract

A novel matrix method based on the Taylor series called Taylor-Splitting Collocation Method is presented to solve linear and nonlinear ordinary differential equations. Unlike the previous approaches, the fundamental matrix equation is reformulated using interval splitting. The residual error estimation algorithm is presented. Convergence analysis is given in a general form. Four different mechanical models are analyzed:1.Forced oscillations of a linear spring-mass model2.Forced oscillations of a nonlinear spring-mass model3.Free oscillations of a cubic nonlinear spring-dashpot-mass model4.Forced oscillations of a damped nonlinear pendulum model

Suggested Citation

  • Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008621
    DOI: 10.1016/j.chaos.2022.112683
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    References listed on IDEAS

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    1. Darae Jeong & Yibao Li & Chaeyoung Lee & Junxiang Yang & Yongho Choi & Junseok Kim, 2019. "Verification of Convergence Rates of Numerical Solutions for Parabolic Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, June.
    2. Alvaro H. Salas & S. A. El-Tantawy & Noufe H. Aljahdaly, 2021. "An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, January.
    3. Berna Bülbül & Mehmet Sezer, 2013. "Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, June.
    4. S. A. El-Tantawy & Alvaro H. Salas & M. R. Alharthi, 2021. "On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, February.
    5. Oğuz, Cem & Sezer, Mehmet, 2015. "Chelyshkov collocation method for a class of mixed functional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 943-954.
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